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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-alalbial | Structured version Visualization version GIF version |
Description: Adding a second quantifier over the same variable is a transparent operation, (∀∀ case). (Contributed by BJ, 20-Oct-2019.) |
Ref | Expression |
---|---|
bj-alalbial | ⊢ (∀𝑥∀𝑥𝜑 ↔ ∀𝑥𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfa1 2147 | . 2 ⊢ Ⅎ𝑥∀𝑥𝜑 | |
2 | 1 | 19.3 2194 | 1 ⊢ (∀𝑥∀𝑥𝜑 ↔ ∀𝑥𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 205 ∀wal 1538 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1912 ax-6 1970 ax-7 2010 ax-10 2136 ax-12 2170 |
This theorem depends on definitions: df-bi 206 df-or 845 df-ex 1781 df-nf 1785 |
This theorem is referenced by: (None) |
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